Mathematics

This is an optimization problem where you're finding the peak of a parabola. Since $A(x) = x(12-2x)$ is a quadratic function that opens downward, its maximum occurs at a single point—either at the vertex or at a boundary. The quickest path is to expand the expression, find where the derivative equals zero, and verify that critical point lies in your domain $[0, 6]$.

This is an optimization problem where you're finding the peak of a parabola. Since $A(x) = x(12-2x)$ is a quadratic function that opens downward, its maximum occurs at a single point—either at the vertex or at a boundary. The quickest path is to expand the expression, find where the derivative equals zero, and verify that critical point lies in your domain $[0, 6]$.